Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 48 minutes and standard deviation 22 minutes. A researcher observed 18 students who entered the library to study. Round all answers to 4 decimal places where possible. If one randomly selected student is timed, find the probability that this student's time will be between 41 and 47 minutes.  For the 18 students, find the probability that their average time studying is between 41 and 47 minutes.  Find the probability that the randomly selected 18 students will have a total study time less than 882 minutes The top 20% of the total study time for groups of 18 students will be given a sticker that says "Great dedication". What is the least total time that a group can study and still receive a sticker?

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